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The Rossiter-McLaughlin (hereafter RM) effect is a key tool for measuring theprojected spin-orbit angle between stellar spin axes and orbits of transitingplanets. However, the measured radial velocity (RV) anomalies produced by thiseffect are not intrinsic and depend on both instrumental resolution and datareduction routines. Using inappropriate formulas to model the RM effectintroduces biases, at least in the projected velocity Vsin(i) compared to thespectroscopic value. Currently, only the iodine cell technique has beenmodeled, which corresponds to observations done by, e.g., the HIRESspectrograph of the Keck telescope. In this paper, we provide a simpleexpression of the RM effect specially designed to model observations done bythe Gaussian fit of a cross-correlation function (CCF) as in the routinesperformed by the HARPS team. We derived also a new analytical formulation ofthe RV anomaly associated to the iodine cell technique. For both formulas, wemodeled the subplanet mean velocity v_p and dispersion beta_p accurately takingthe rotational broadening on the subplanet profile into account. We compare ourformulas adapted to the CCF technique with simulated data generated with thenumerical software SOAP-T and find good agreement up to Vsin(i) < 20 km/s. Incontrast, the analytical models simulating the two different observationtechniques can disagree by about 10 sigma in Vsin(i) for large spin-orbitmisalignments. It is thus important to apply the adapted model when fittingdata.

New analytical expressions of the Rossiter-McLaughlin effect adapted to different observation techniques